ps3-solution

ps3-solution - Econ 805 Problem Set 3 Solution 1. (Gibbons...

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Econ 805 Problem Set 3 Solution 1. (Gibbons 1.2). In the following game, what strategies survive IESDS (iterated elimination of strictly dominated strategies)? What are the pure strategy Nash equilibria? LCR T 2 , 01 , 14 , 2 M 3 , 4 1 , 22 , 3 B 1 , 3 0 , 23 , 0 Answer: for player 1, B is strictly dominated by T . Sowecande letetherowo f B . Thenforp layer2 , C is strictly dominated by R . No further strategies can be deleted. Therefore, the strategies that survive IESDS are: ( T,M ) and ( L, R ) . ThepurestrategyNEo fth isgameare ( M,L ) and ( T,R ) (see the underscore in the bi-matrix). 2. Mascolell 8.B.5. Answer: (i) First, any quantity q>q m = a c 2 b (the monopoly quantity) is strictly dominated by q m . Then the remaining strategy set for each f rm is [0 ,q m ] .N o wy o u can calculate the best response to q m .Y o uw i l lg e t R ( q m )= a c 2 b q m 2 .. One can show that any q<b ( q m ) is strictly dominated by R ( q m ) . Now the relevant strategy set is [ R ( q m ) ,q m ] . Now you can calculate the best response to R ( q m ) . You can easily get that R 2 ( q m )= a c 2 b R ( q m ) 2 . Again you can prove that any quantity q>R 2 ( q m ) is strictly dominated by R 2 ( q m ) . Now the relevant strategy set shrinks to [ R ( q m ) ,R 2 ( q m )] .I fy o u continue this process, after 2 n rounds of IESDS, the remaining strategy set is [ R 2 n 1 ( q m ) , R 2 n ( q m )] . Nowyouon lyneedtoshowthat R n ( q m ) converges as n goes to in f nity. You can show that R n ( q m )= 2 n 2 n 1 +2 n 2 + ... +( 1) n 2 n n 2 n q m =[ 1 1 2 + 1 4 ...
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This note was uploaded on 01/27/2011 for the course ECON 805 taught by Professor Zeca during the Spring '08 term at UConn.

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ps3-solution - Econ 805 Problem Set 3 Solution 1. (Gibbons...

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